A194524 - OEIS

%I #16 Dec 29 2020 10:21:23

%S 2,4,-1,1,3,-2,0,2,4,-1,1,3,5,0,2,4,-1,1,3,5,0,2,4,6,1,3,5,0,2,4,6,1,

%T 3,5,7,2,4,6,1,3,5,7,2,4,6,8,3,5,7,2,4,6,8,3,5,7,9,4,6,8,3,5,7,9,4,6,

%U 8,10,5,7,9,4,6,8,10,5,7,9,11,6,8,10,5,7,9,11,6,8,10,12,7,9,11,6,8

%N First coordinate of (4,7)-Lagrange pair for n.

%C See A194508.

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,1,-1).

%F From _Chai Wah Wu_, Jan 21 2020: (Start)

%F a(n) = a(n-1) + a(n-11) - a(n-12) for n > 12.

%F G.f.: x*(2*x^10 - 5*x^9 + 2*x^8 + 2*x^7 + 2*x^6 - 5*x^5 + 2*x^4 + 2*x^3 - 5*x^2 + 2*x + 2)/(x^12 - x^11 - x + 1). (End)

%F a(n) = 2*n - 7*floor((3*n + 4)/11). - _Ridouane Oudra_, Dec 29 2020

%e This table shows (x(n),y(n)) for 1<=n<=13:

%e n..... 1..2..3..4..5..6..7..8..9..10..11..12..13

%e x(n).. 2..4.-1..1..3.-2..0..2..4.-1...1...3...5

%e y(n). -1.-2..1..0.-1..2..1..0.-1..2...1...0..-1

%t c = 4; d = 7;

%t x1 = {2, 4, -1, 1, 3, -2, 0, 2, 4, -1, 1};

%t y1 = {-1, -2, 1, 0, -1, 2, 1, 0, -1, 2, 1};

%t x[n_] := If[n <= c + d, x1[[n]], x[n - c - d] + 1]

%t y[n_] := If[n <= c + d, y1[[n]], y[n - c - d] + 1]

%t Table[x[n], {n, 1, 100}]  (* A194524 *)

%t Table[y[n], {n, 1, 100}]  (* A194525 *)

%t r[1, n_] := n; r[2, n_] := x[n]; r[3, n_] := y[n]

%t TableForm[Table[r[m, n], {m, 1, 3}, {n, 1, 30}]]

%Y Cf. A194508, A194525.

%K sign

%O 1,1

%A _Clark Kimberling_, Aug 28 2011